Asymptotic behaviour of solutions to the massive Vlasov-Nordstrom system

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Written by Jeremie Joudioux

I will present  a global existence result for the massive Vlasov-Nordstrom system, in dimension 4+1, for small initial data, and will describe the asymptotic behavior of solutions of this system. The method is based on the contruction of commutators for the linear massive transport equation. This techniques of commutators is widely inspired by similar techniques developed by Klainerman for the wave equation, known as the vector fields methods.
After explaining the decay of solutions of the linear massive transport equation, I will explain how this result applies to the massive Vlasov-Nordstrom system in dimension 4+1. I will finally explain how these techniques can be adapted to deal with the 3+1 Vlasov-Nordstrom system.
This work is a collaboration with D. Fajman (Vienna), and J. Smulevici (Orsay).